Best way to move same content over to new domain?

Hey,

Alright, let's say I have a very basic 5 page website offering some services, and let's just pretend it's all on myolddomain.com. Now I formed an LLC and have a much better name and want to move the whole site over to mybetterdomain.com.

Now Google has already indexed everything over at myolddomain.com, so if I was to just move the whole site over to mybetterdomain.com, I am guessing Google would just see that as dupe content for the new domain, and not allow any of the pages to be indexed... and even if they were indexed, they wouldn't have a very good ranking.

So what would be the best way to move this old site, over to my new domain name without any dupe content issues?

Would it be to just 301 redirect anyone who tries to go to myolddomain.com over to mynewdomain.com?

Are you using Google webmaster tool..
There is option to update your new address to Google.
so make a 301 redirect and then update new address in GWT.

In site configuration, click on change of address and you will find all the information-

For best results, follow these steps:
Set up the new site
Review our guidelines for moving your site to a new domain. Set up your content on your new domain, then make sure all internal links point to the new domain.
Redirect all traffic from the old site
Use a 301 redirect to permanently redirect the pages on your old site to your new site. This tells users and search engines that your site has permanently moved. Ask webmasters to update their links to point to your new domain and make sure incoming links to your old site are redirected correctly using the 301 redirects.
Add your new site to Webmaster Tools
Make sure you have added and verified your new domain.
Tell us the URL of your new domain